Why evolution does not always lead to an optimal proto-language.An approach based on the replicator dynamics

Sender–receiver models in the style of Lewis (1969), Hurford (1989), or Nowak and Krakauer (1999) can be used to explain meaning of signals in situations of cooperative interaction. Importantly, meaning here is not an ex–ante concept, but arises as an equilibrium property of a game. A strategy of this game is a pair of a sender and a receiver matrix, where the sender matrix links events that possibly become the object of communication to signals, and the receiver matrix links potentially received signals to events. A Nash equilibrium strategy of this game can be interpreted as a so–called proto–language, that is, a set of event–signals relations that facilitate communication over a finite number of events. A typical property of this game is that it admits a multiplicity of Nash equilibrium components, where two (or more) events share the use of one signal or where two (or more) signals are associated with the same event, leading to a situation where some of the potential of communication if left unexploited. W¨arneryd (1993) as well as Trapa and Nowak (2000) show that only the strict Nash strategies, where each event is bijectively linked to one signal and where the inverse of this mapping is used to associate signals with events, which therefore guarantee the full potential of communication, are evolutionarily stable. Evolutionary stability implies asymptotic stability in the replicator dynamics. Interestingly, simulations with this model in the style of a replicator dynamics as reported in Nowak and Krakauer (1999) typically give rise to a suboptimal proto–language, where more than one event is linked to the same signal whereas another signal remains idle. In view of W¨arneryd (1993) and Trapa and Nowak (2000) this raises the following questions: Does this reflect generic behavior of the replicator dynamics for this model? And, if so, what are the properties of a strategy that can protect itself from being driven out by this dynamics despite the fact that it cannot be evolutionarily stable? This paper gives answers to these questions in terms of neutral stability and its dynamic consequences. It, first, provides a complete characterization of neutrally stable strategies for this game, showing that in such a situation, indeed, there can be two (or more) events that are linked to the same signal or two (or more) signals that are linked to the same event, as long as the degree of ambiguity is not too high. Second, it analyzes the long–run behavior of the replicator dynamics of this model. This essentially derives from neutral stability together with the symmetry properties of this game. Building on a result by Bomze (2002), which establishes equivalence of neutral stability and Lyapunov stability in the replicator dynamics for doubly symmetric games with pairwise interaction, it can be shown that the replicator dynamics of this model does not necessarily lead to an optimal proto–language, but that it can be trapped in situations of ambiguous event–signal relations, where some of the potential of communication is left unexploited.

How much ambiguity can persist? A complete characterization of neutrally stable states for an evolutionary proto-language game

In an evolutionary sender–receiver game that describes how signals become associated with objects (Hurford, 1989; Nowak and Krakauer, 1999), the set of evolutionarily stable states coincides with the set of strict Nash strategies—and a language is a strict Nash strategy if and only if it links each possible referent exclusively to 1 signal and vice versa (Trapa and Nowak, 2000). As a consequence, a language that displays homonymy (or synonymy)—the property that one signal is linked to more than one referent (or one referent to more than one signal)—cannot be an evolutionarily stable state. This seems to conflict with the results of the computer simulation reported in Nowak and Krakauer (1999) that lend support to the conjecture that a language in which the same signal is used for more than one object can be evolutionarily stable. This paper provides necessary and sucient conditions for a neutrally stable state of this game—and, importantly, these conditions directly characterize a single strategy—showing that a language displaying homonymy or synonymy, even though it fails to be evolutionarily stable (in the strict sense), may still satisfy neutral stability, explaining why an evolutionary process does not necessarily lead away from it.

Doves and hawks in economics revisited. An evolutionary quantum game theory-based analysis of financial crises

The last financial and economic crisis demonstrated the dysfunctional long-term effects of aggressive behaviour in financial markets. Yet, evolutionary game theory predicts that under the condition of strategic dependence a certain degree of aggressive behaviour remains within a given population of agents. However, as the consequences of the financial crisis exhibit, it would be desirable to change the 'rules of the game' in a way that prevents the occurrence of any aggressive behaviour and thereby also the danger of market crashes. The paper picks up this aspect. Through the extension of the in literature well-known Hawk-Dove game by a quantum approach, we can show that dependent on entanglement, also evolutionary stable strategies can emerge, which are not predicted by classical evolutionary game theory and where the total economic population uses a non aggressive quantum strategy

Evolutionary dynamics of Lewis signaling games: signaling systems vs. partial pooling

Transfer of information between senders and receivers, of one kind or another, is essential to all life. David Lewis introduced a game theoretic model of the simplest case, where one sender and one receiver have pure common interest. How hard or easy is it for evolution to achieve information transfer in Lewis signaling?. The answers involve surprising subtleties. We discuss some if these in terms of evolutionary dynamics in both finite and infinite populations, with and without mutation

Making See: A Structural Analysis of Mathematical and in Particular Game-Theoretic Writing

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Strategic manipulation in Bayesian dialogues

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Why evolution does not always lead to an optimal signaling system

This paper gives a complete characterization of neutrally stable strategies for sender-receiver games in the style of Lewis, or Nowak and Krakauer [Lewis, D., 1969. Convention: A Philosophical Study. Harvard Univ. Press, Cambridge, MA; Nowak, M., Krakauer, D., 1999. The evolution of language. Proc. Nat. Acad. Sci. USA 96, 8028-8033]. Due to the dynamic implications of neutral stability, the replicator dynamics of this model does not necessarily lead to the rise of an optimal signaling system, where every state of the world is bijectively linked to one signal and vice versa, but it can be trapped in suboptimum situations where two (or more) signals are used for the same event, or two (or more) events are associated with one and the same signal.